B-Spline Basis Functions

B-splines of polynomial order are the unique functions that are globally in and piecewise polynomial of degree . A B-spline of order is fixed when knots are given: the conditions generate a set of equations that is uniquely solved, up to normalization. The normalization is such that all B-splines with respect to a knot sequence form a partition of unity: they sum up to 1. (On the boundaries of the knot sequence, this does not hold.)